package com.actelion.research.calc;


   /** Singular Value Decomposition.
   <P>
   For an m-by-n matrix A with m >= n, the singular value decomposition is
   an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and
   an n-by-n orthogonal matrix V so that A = U*S*V'.
   <P>
   The singular values, sigma[k] = S[k][k], are ordered so that
   sigma[0] >= sigma[1] >= ... >= sigma[n-1].
   <P>
   The singular value decompostion always exists, so the constructor will
   never fail.  The matrix condition number and the effective numerical
   rank can be computed from this decomposition.
   */

public class SingularValueDecomposition implements java.io.Serializable {
    static final long serialVersionUID = 0x20110324;

/* ------------------------
   Class variables
 * ------------------------ */

   /** Arrays for internal storage of U and V.
   @serial internal storage of U.
   @serial internal storage of V.
   */
   private double[][] U, V;

   /** Array for internal storage of singular values.
   @serial internal storage of singular values.
   */
   private double[] s;

   /** Row and column dimensions.
   @serial row dimension.
   @serial column dimension.
   */
   private int m, n;

/* ------------------------
   Constructor
 * ------------------------ */

   /** Construct the singular value decomposition
   @param Arg    Rectangular matrix
   @return     Structure to access U, S and V.
   */

   public SingularValueDecomposition (double[][] A, ProgressListener progressListener, ThreadMaster threadMaster) {

	  // Derived from LINPACK code.
	  // Initialize.
	  m = A.length;
	  n = A[0].length;
	  int nu = Math.min(m,n);
	  s = new double [Math.min(m+1,n)];
	  U = new double [m][nu];
	  V = new double [n][n];
	  double[] e = new double [n];
	  double[] work = new double [m];
	  boolean wantu = true;
	  boolean wantv = true;

	  // Reduce A to bidiagonal form, storing the diagonal elements
	  // in s and the super-diagonal elements in e.

	  int nct = Math.min(m-1,n);
	  int nrt = Math.max(0,Math.min(n-2,m));

	  if (progressListener != null)
		progressListener.startProgress("Initializing SVD...", 0, Math.max(nct,nrt));

	  for (int k = 0; k < Math.max(nct,nrt); k++) {
		if (progressListener != null)
		  progressListener.updateProgress(k);
		if (threadMaster != null && threadMaster.threadMustDie())
		  return;

		 if (k < nct) {

			// Compute the transformation for the k-th column and
			// place the k-th diagonal in s[k].
			// Compute 2-norm of k-th column without under/overflow.
			s[k] = 0;
			for (int i = k; i < m; i++) {
			   s[k] = hypot(s[k],A[i][k]);
			}
			if (s[k] != 0.0) {
			   if (A[k][k] < 0.0) {
				  s[k] = -s[k];
			   }
			   for (int i = k; i < m; i++) {
				  A[i][k] /= s[k];
			   }
			   A[k][k] += 1.0;
			}
			s[k] = -s[k];
		 }
		 for (int j = k+1; j < n; j++) {
			if ((k < nct) & (s[k] != 0.0))  {

			// Apply the transformation.

			   double t = 0;
			   for (int i = k; i < m; i++) {
				  t += A[i][k]*A[i][j];
			   }
			   t = -t/A[k][k];
			   for (int i = k; i < m; i++) {
				  A[i][j] += t*A[i][k];
			   }
			}

			// Place the k-th row of A into e for the
			// subsequent calculation of the row transformation.

			e[j] = A[k][j];
		 }
		 if (wantu & (k < nct)) {

			// Place the transformation in U for subsequent back
			// multiplication.

			for (int i = k; i < m; i++) {
			   U[i][k] = A[i][k];
			}
		 }
		 if (k < nrt) {

			// Compute the k-th row transformation and place the
			// k-th super-diagonal in e[k].
			// Compute 2-norm without under/overflow.
			e[k] = 0;
			for (int i = k+1; i < n; i++) {
			   e[k] = hypot(e[k],e[i]);
			}
			if (e[k] != 0.0) {
			   if (e[k+1] < 0.0) {
				  e[k] = -e[k];
			   }
			   for (int i = k+1; i < n; i++) {
				  e[i] /= e[k];
			   }
			   e[k+1] += 1.0;
			}
			e[k] = -e[k];
			if ((k+1 < m) & (e[k] != 0.0)) {

			// Apply the transformation.

			   for (int i = k+1; i < m; i++) {
				  work[i] = 0.0;
			   }
			   for (int j = k+1; j < n; j++) {
				  for (int i = k+1; i < m; i++) {
					 work[i] += e[j]*A[i][j];
				  }
			   }
			   for (int j = k+1; j < n; j++) {
				  double t = -e[j]/e[k+1];
				  for (int i = k+1; i < m; i++) {
					 A[i][j] += t*work[i];
				  }
			   }
			}
			if (wantv) {

			// Place the transformation in V for subsequent
			// back multiplication.

			   for (int i = k+1; i < n; i++) {
				  V[i][k] = e[i];
			   }
			}
		 }
	  }

	  // Set up the final bidiagonal matrix or order p.

	  int p = Math.min(n,m+1);
	  if (nct < n) {
		 s[nct] = A[nct][nct];
	  }
	  if (m < p) {
		 s[p-1] = 0.0;
	  }
	  if (nrt+1 < p) {
		 e[nrt] = A[nrt][p-1];
	  }
	  e[p-1] = 0.0;

	  // If required, generate U.

	  if (wantu) {
		if (progressListener != null)
		  progressListener.startProgress("generating eigenvalues...", 0, nct);

		  for (int j = nct; j < nu; j++) {
			for (int i = 0; i < m; i++) {
			   U[i][j] = 0.0;
			}
			U[j][j] = 1.0;
		 }
		 for (int k = nct-1; k >= 0; k--) {
			if (progressListener != null)
			  progressListener.updateProgress(nct-k);
			if (threadMaster != null && threadMaster.threadMustDie())
			  return;

			if (s[k] != 0.0) {
			   for (int j = k+1; j < nu; j++) {
				  double t = 0;
				  for (int i = k; i < m; i++) {
					 t += U[i][k]*U[i][j];
				  }
				  t = -t/U[k][k];
				  for (int i = k; i < m; i++) {
					 U[i][j] += t*U[i][k];
				  }
			   }
			   for (int i = k; i < m; i++ ) {
				  U[i][k] = -U[i][k];
			   }
			   U[k][k] = 1.0 + U[k][k];
			   for (int i = 0; i < k-1; i++) {
				  U[i][k] = 0.0;
			   }
			} else {
			   for (int i = 0; i < m; i++) {
				  U[i][k] = 0.0;
			   }
			   U[k][k] = 1.0;
			}
		 }
	  }

	  // If required, generate V.

	  if (wantv) {
		if (progressListener != null)
		  progressListener.startProgress("generating eigenvectors...", 0, n);

		 for (int k = n-1; k >= 0; k--) {
			if (progressListener != null)
			  progressListener.updateProgress(n-k);
			if (threadMaster != null && threadMaster.threadMustDie())
			  return;

			if ((k < nrt) & (e[k] != 0.0)) {
			   for (int j = k+1; j < nu; j++) {
				  double t = 0;
				  for (int i = k+1; i < n; i++) {
					 t += V[i][k]*V[i][j];
				  }
				  t = -t/V[k+1][k];
				  for (int i = k+1; i < n; i++) {
					 V[i][j] += t*V[i][k];
				  }
			   }
			}
			for (int i = 0; i < n; i++) {
			   V[i][k] = 0.0;
			}
			V[k][k] = 1.0;
		 }
	  }

	  // Main iteration loop for the singular values.

	  int pp = p-1;
	  int iter = 0;
	  double eps = Math.pow(2.0,-52.0);

	  if (progressListener != null)
		progressListener.startProgress("locating negligible elements...", 0, pp+1);

	  while (p > 0) {
		if (progressListener != null)
		  progressListener.updateProgress(pp-p);
		if (threadMaster != null && threadMaster.threadMustDie())
		  return;

		 int k,kase;

		 // Here is where a test for too many iterations would go.

		 // This section of the program inspects for
		 // negligible elements in the s and e arrays.  On
		 // completion the variables kase and k are set as follows.

		 // kase = 1     if s(p) and e[k-1] are negligible and k<p
		 // kase = 2     if s(k) is negligible and k<p
		 // kase = 3     if e[k-1] is negligible, k<p, and
		 //              s(k), ..., s(p) are not negligible (qr step).
		 // kase = 4     if e(p-1) is negligible (convergence).

		 for (k = p-2; k >= -1; k--) {
			if (k == -1) {
			   break;
			}
			if (Math.abs(e[k]) <= eps*(Math.abs(s[k]) + Math.abs(s[k+1]))) {
			   e[k] = 0.0;
			   break;
			}
		 }
		 if (k == p-2) {
			kase = 4;
		 } else {
			int ks;
			for (ks = p-1; ks >= k; ks--) {
			   if (ks == k) {
				  break;
			   }
			   double t = (ks != p ? Math.abs(e[ks]) : 0.) +
						  (ks != k+1 ? Math.abs(e[ks-1]) : 0.);
			   if (Math.abs(s[ks]) <= eps*t)  {
				  s[ks] = 0.0;
				  break;
			   }
			}
			if (ks == k) {
			   kase = 3;
			} else if (ks == p-1) {
			   kase = 1;
			} else {
			   kase = 2;
			   k = ks;
			}
		 }
		 k++;

		 // Perform the task indicated by kase.

		 switch (kase) {

			// Deflate negligible s(p).

			case 1: {
			   double f = e[p-2];
			   e[p-2] = 0.0;
			   for (int j = p-2; j >= k; j--) {
				  double t = hypot(s[j],f);
				  double cs = s[j]/t;
				  double sn = f/t;
				  s[j] = t;
				  if (j != k) {
					 f = -sn*e[j-1];
					 e[j-1] = cs*e[j-1];
				  }
				  if (wantv) {
					 for (int i = 0; i < n; i++) {
						t = cs*V[i][j] + sn*V[i][p-1];
						V[i][p-1] = -sn*V[i][j] + cs*V[i][p-1];
						V[i][j] = t;
					 }
				  }
			   }
			}
			break;

			// Split at negligible s(k).

			case 2: {
			   double f = e[k-1];
			   e[k-1] = 0.0;
			   for (int j = k; j < p; j++) {
				  double t = hypot(s[j],f);
				  double cs = s[j]/t;
				  double sn = f/t;
				  s[j] = t;
				  f = -sn*e[j];
				  e[j] = cs*e[j];
				  if (wantu) {
					 for (int i = 0; i < m; i++) {
						t = cs*U[i][j] + sn*U[i][k-1];
						U[i][k-1] = -sn*U[i][j] + cs*U[i][k-1];
						U[i][j] = t;
					 }
				  }
			   }
			}
			break;

			// Perform one qr step.

			case 3: {

			   // Calculate the shift.

			   double scale = Math.max(Math.max(Math.max(Math.max(
					   Math.abs(s[p-1]),Math.abs(s[p-2])),Math.abs(e[p-2])),
					   Math.abs(s[k])),Math.abs(e[k]));
			   double sp = s[p-1]/scale;
			   double spm1 = s[p-2]/scale;
			   double epm1 = e[p-2]/scale;
			   double sk = s[k]/scale;
			   double ek = e[k]/scale;
			   double b = ((spm1 + sp)*(spm1 - sp) + epm1*epm1)/2.0;
			   double c = (sp*epm1)*(sp*epm1);
			   double shift = 0.0;
			   if ((b != 0.0) | (c != 0.0)) {
				  shift = Math.sqrt(b*b + c);
				  if (b < 0.0) {
					 shift = -shift;
				  }
				  shift = c/(b + shift);
			   }
			   double f = (sk + sp)*(sk - sp) + shift;
			   double g = sk*ek;

			   // Chase zeros.

			   for (int j = k; j < p-1; j++) {
				  double t = hypot(f,g);
				  double cs = f/t;
				  double sn = g/t;
				  if (j != k) {
					 e[j-1] = t;
				  }
				  f = cs*s[j] + sn*e[j];
				  e[j] = cs*e[j] - sn*s[j];
				  g = sn*s[j+1];
				  s[j+1] = cs*s[j+1];
				  if (wantv) {
					 for (int i = 0; i < n; i++) {
						t = cs*V[i][j] + sn*V[i][j+1];
						V[i][j+1] = -sn*V[i][j] + cs*V[i][j+1];
						V[i][j] = t;
					 }
				  }
				  t = hypot(f,g);
				  cs = f/t;
				  sn = g/t;
				  s[j] = t;
				  f = cs*e[j] + sn*s[j+1];
				  s[j+1] = -sn*e[j] + cs*s[j+1];
				  g = sn*e[j+1];
				  e[j+1] = cs*e[j+1];
				  if (wantu && (j < m-1)) {
					 for (int i = 0; i < m; i++) {
						t = cs*U[i][j] + sn*U[i][j+1];
						U[i][j+1] = -sn*U[i][j] + cs*U[i][j+1];
						U[i][j] = t;
					 }
				  }
			   }
			   e[p-2] = f;
			   iter = iter + 1;
			}
			break;

			// Convergence.

			case 4: {

			   // Make the singular values positive.

			   if (s[k] <= 0.0) {
				  s[k] = (s[k] < 0.0 ? -s[k] : 0.0);
				  if (wantv) {
					 for (int i = 0; i <= pp; i++) {
						V[i][k] = -V[i][k];
					 }
				  }
			   }

			   // Order the singular values.

			   while (k < pp) {
				  if (s[k] >= s[k+1]) {
					 break;
				  }
				  double t = s[k];
				  s[k] = s[k+1];
				  s[k+1] = t;
				  if (wantv && (k < n-1)) {
					 for (int i = 0; i < n; i++) {
						t = V[i][k+1]; V[i][k+1] = V[i][k]; V[i][k] = t;
					 }
				  }
				  if (wantu && (k < m-1)) {
					 for (int i = 0; i < m; i++) {
						t = U[i][k+1]; U[i][k+1] = U[i][k]; U[i][k] = t;
					 }
				  }
				  k++;
			   }
			   iter = 0;
			   p--;
			}
			break;
		 }
	  }
   }

/* ------------------------
   Public Methods
 * ------------------------ */

   /** Return the left singular vectors
   @return     U
   */

   public double[][] getU () {
//	   return new Matrix(U);
	   return U;
   }

   /** Return the right singular vectors
   @return     V
   */

   public double[][] getV () {
//	   return new Matrix(V,n,n);
	   return V;
   }

   /** Return the one-dimensional array of singular values
   @return     diagonal of S.
   */

   public double[] getSingularValues () {
	  return s;
   }

   /** Return the diagonal matrix of singular values
   @return     S
   */

/* public Matrix getS () {
	  Matrix X = new Matrix(n,n);
	  for (int i = 0; i < n; i++) {
		 for (int j = 0; j < n; j++) {
			X.set(i,j,0.0);
		 }
		 X.set(i,i,this.s[i]);
	  }
	  return X;
   }*/

   /** Two norm
   @return     max(S)
   */

   public double norm2 () {
	  return s[0];
   }

   /** Two norm condition number
   @return     max(S)/min(S)
   */

   public double cond () {
	  return s[0]/s[Math.min(m,n)-1];
   }

   /** Effective numerical matrix rank
   @return     Number of nonnegligible singular values.
   */

   public int rank () {
	  double eps = Math.pow(2.0,-52.0);
	  double tol = Math.max(m,n)*s[0]*eps;
	  int r = 0;
	  for (int i = 0; i < s.length; i++) {
		 if (s[i] > tol) {
			r++;
		 }
	  }
	  return r;
   }

   public static double hypot(double a, double b) {
      double r;
      if (Math.abs(a) > Math.abs(b)) {
         r = b/a;
         r = Math.abs(a)*Math.sqrt(1+r*r);
      } else if (b != 0) {
         r = a/b;
         r = Math.abs(b)*Math.sqrt(1+r*r);
      } else {
         r = 0.0;
      }
      return r;
   }
}
